Showing papers in "European Journal of Combinatorics in 1982"

TL;DR: This result generalizes a theorem of Bollobas that says that positive integers can be positive integers for every i = 1, ..., m and i m ≤ ( r + s s ) .

TL;DR: In this work, the generalized hexagon on 819 points, with parameters (2, 8), is included as a 5-design in the Cayley Plane OP, meeting the absolute bound.

TL;DR: It is proved that there are always edges h from some u to z and k from z to some v such that minz≠x≡v≠v λ(x, y; D) = z≡x≠ v≠V A(x- y; Dhk), where Dhk denotes the digraph which arises from D by deleting h and k and adding a new edge from u to v.

TL;DR: This conjecture that, unless G belongs to a known class of exceptions, almost all Cayley graphs of G have G for their full automorphism group is proved for nilpotent groups of odd order.

TL;DR: The first section of this paper shows that the bipartite Ramsey number br ( m, n ) satisfies the inequality, and gives a conjecture for the Ramsey numbers of the complete graphs, and the numbers of monochromatic K 4 s in certain colourings of K′ are investigated.

TL;DR: A q-analogue of the Kummer congruences of the Euler numbers is proposed for the study of the q-Euler numbers and a double sequence of polynomials arises naturally in this context.

TL;DR: This paper shows that similar properties of k-optimal partitions for the graph of a partially ordered set also hold for several classes of graphs.

TL;DR: It is shown that for a wide class of sequences {ai} of positive integers, the polynomials Π i = 1 n ( 1 + x a i ) = ∑ k = 0 N b k x k , N =∑ i =1 n a i are almost unimodal.

TL;DR: This work establishes a new geometrical characterization of oriented matroids of rank 3 and describes the relationship between these characterizations and the first and second Coxeter's projective diagrams of zonohedra.

TL;DR: One of the important properties of linear partitions is that their generating function can be written as a function of integers.

TL;DR: It is shown that there are many (ℵ 1 ) X 's which can not be decomposed into the union of regular k i -gons where k i ⩾ ( t + 1).

TL;DR: This paper shows how the greater index of a sequence may be decomposed and reassembled to form a Durfee dissection partition, and these correspondences are used to interpret some of Slater's identities as generating functions for sets of partitions.

TL;DR: It is proved that there is a finite family F of graphs such that any graph G with minimum degree at least 69 is the intersection graph of a 3-uniform linear hypergraph if and only if G has no induced subgraph isomorphic to a member of F .

TL;DR: This paper extends the enumeration to dimension 23, finding 40 lattices of dimension 21, 68 of dimension 22, and 117 of dimension 23 and gives explicit formulae for the Minkowski-Siegel mass constants for unimodular lattices and an exact table of the mass constants up to 32 dimensions.

TL;DR: An efficient algorithm is described for testing regularity of a matroid (i.e., representability over every field) and a number of other matroid representability questions cannot be decided efficiently.

TL;DR: A detailed study of group partitions having this latter property is made, and the results of exhaustive searches for partitions of this type are reported which yield improved lower bounds for certain of these Ramsey numbers.

TL;DR: The purpose of this paper is to give the proof of [5, Theorem 4.2], to give a systematic method of constructing a solution of Problem B using flats and spreads in a finite projective geometry.

TL;DR: Ein entsprechendes Resultat fUr Mengen ist der zum Allgemeingut der Kombinatorik gehorende Satz von Ramsey für eine gemeinsame Verallgemeinerung dieser Ergebnisse.

TL;DR: The structure of the lattice of all subposets of a fixed poset is explored and this lattice is then used to prove some identities for the order polynomial of that poset.

TL;DR: A direct proof of the identity Pn (−1)=En where Pn(t) is the inversion enumerator polynomial for labelled trees and En is the nth Euler number.

TL;DR: Subgeometries PG(r, √q) of PG (r, q), q a square, r ⩾ 3, are characterized as k-sets of type (m, n) with respect to primes and an infinite family of two character sets in PG ( r, q, r odd, q asquare, is constructed.

TL;DR: It is proved that if q + 1 = 2p, p(⩾5) an odd prime, then |K|⩽|K∩Q| + 4.

TL;DR: A complete classification has been made of all finite incidence structures of points and circles such that the residual structure with respect to an arbitrary point is always some Dembowski semi-plane.

TL;DR: Given a pair of finite lattices ( L, L * ), a necessary condition is proved for the existence of a graph G with non-adjacent vertices a and b, having L as its lattice of cutsets and L * as its clustering of minimal cutsets.

TL;DR: Let S; be an n x n square array of lattice points in the plane and g(n) be the size of a smallest subset X of S which does not contain the vertices of a square with its sides parallel to the sides of S; but which is such that the addition of any new point to X forces the appearance of such a square.

TL;DR: This paper gives a direct combinatorial method for obtaining the homomorphic image of a frame in the ring Z[x1x2, ...] of polynomials in an infinite sequence of independent indeterminates xi and gives a combinatorsial interpretation to the non-zero terms that arise from the classical expression for a skew Schur function.